EdDSA.cs

using System;
using System.IO;
using System.Numerics;
using Waher.Runtime.Temporary;
 
namespace Waher.Security.EllipticCurves
{
    public static class EdDSA
    {
        public static byte[] Sign(byte[] Data, byte[] PrivateKey, byte[] Prefix,
            HashFunctionArray HashFunction, EdwardsCurveBase Curve)
        {
            // 5.1.6 of RFC 8032
 
            int ScalarBytes = PrivateKey.Length;
 
            if (Prefix.Length != ScalarBytes)
                throw new ArgumentException("Invalid prefix.", nameof(Prefix));
 
            BigInteger a = EllipticCurve.ToInt(PrivateKey);
            PointOnCurve P = Curve.ScalarMultiplication(PrivateKey, Curve.BasePoint, true);
            byte[] A = Encode(P, Curve);
            int c = Data.Length;
            byte[] Bin = new byte[ScalarBytes + c];             // dom2(F, C) = blank string
            Array.Copy(Prefix, 0, Bin, 0, ScalarBytes);         // prefix
            Array.Copy(Data, 0, Bin, ScalarBytes, c);           // PH(M)=M
 
            byte[] h = HashFunction(Bin);
            BigInteger r = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
            PointOnCurve R = Curve.ScalarMultiplication(r, Curve.BasePoint, true);
            byte[] Rs = Encode(R, Curve);
 
            Bin = new byte[(ScalarBytes << 1) + c];             // dom2(F, C) = blank string
            Array.Copy(Rs, 0, Bin, 0, ScalarBytes);
            Array.Copy(A, 0, Bin, ScalarBytes, ScalarBytes);
            Array.Copy(Data, 0, Bin, ScalarBytes << 1, c);      // PH(M)=M
 
            h = HashFunction(Bin);
 
            BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
            BigInteger s = Curve.ModulusN.Add(r, Curve.ModulusN.Multiply(k, a));
 
            Bin = s.ToByteArray();
            if (Bin.Length != ScalarBytes)
                Array.Resize(ref Bin, ScalarBytes);
 
            byte[] Signature = new byte[ScalarBytes << 1];
 
            Array.Copy(Rs, 0, Signature, 0, ScalarBytes);
            Array.Copy(Bin, 0, Signature, ScalarBytes, ScalarBytes);
 
            return Signature;
        }
 
        public static byte[] Sign(Stream Data, byte[] PrivateKey, byte[] Prefix,
            HashFunctionStream HashFunction, EdwardsCurveBase Curve)
        {
            // 5.1.6 of RFC 8032
 
            int ScalarBytes = PrivateKey.Length;
 
            if (Prefix.Length != ScalarBytes)
                throw new ArgumentException("Invalid prefix.", nameof(Prefix));
 
            BigInteger a = EllipticCurve.ToInt(PrivateKey);
            PointOnCurve P = Curve.ScalarMultiplication(PrivateKey, Curve.BasePoint, true);
            byte[] A = Encode(P, Curve);
            byte[] h;
 
            using (TemporaryStream TempFile = new TemporaryStream())    // dom2(F, C) = blank string
            {
                TempFile.Write(Prefix, 0, ScalarBytes);             // prefix
                
                Data.Position = 0;
                Data.CopyTo(TempFile);                              // PH(M)=M
 
                TempFile.Position = 0;
                h = HashFunction(TempFile);
            }
            
            BigInteger r = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
            PointOnCurve R = Curve.ScalarMultiplication(r, Curve.BasePoint, true);
            byte[] Rs = Encode(R, Curve);
 
            using (TemporaryStream TempFile = new TemporaryStream())    // dom2(F, C) = blank string
            {
                TempFile.Write(Rs, 0, ScalarBytes);
                TempFile.Write(A, 0, ScalarBytes);
 
                Data.Position = 0;
                Data.CopyTo(TempFile);                              // PH(M)=M
 
                TempFile.Position = 0;
                h = HashFunction(TempFile);
            }
 
            BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
            BigInteger s = Curve.ModulusN.Add(r, Curve.ModulusN.Multiply(k, a));
 
            byte[] Bin = s.ToByteArray();
            if (Bin.Length != ScalarBytes)
                Array.Resize(ref Bin, ScalarBytes);
 
            byte[] Signature = new byte[ScalarBytes << 1];
 
            Array.Copy(Rs, 0, Signature, 0, ScalarBytes);
            Array.Copy(Bin, 0, Signature, ScalarBytes, ScalarBytes);
 
            return Signature;
        }
 
        public static byte[] Encode(PointOnCurve P, EdwardsCurveBase Curve)
        {
            int ScalarBits = Curve.CoordinateBits;
            int ScalarBytes = (ScalarBits + 9) >> 3;
 
            byte[] y = P.Y.ToByteArray();
            if (y.Length != ScalarBytes)
                Array.Resize(ref y, ScalarBytes);
 
            byte[] x = P.X.ToByteArray();
            int Msb = (ScalarBits + 1) & 7;
 
            byte Mask = (byte)(0xff >> (8 - Msb));
            y[ScalarBytes - 1] &= Mask;
 
            if ((x[0] & 1) != 0)
                y[ScalarBytes - 1] |= 0x80;     // Always MSB
 
            return y;
        }
 
        public static PointOnCurve Decode(byte[] Encoded, EdwardsCurveBase Curve)
        {
            int ScalarBits = Curve.CoordinateBits;
            int ScalarBytes = (ScalarBits + 9) >> 3;
 
            if (Encoded.Length != ScalarBytes)
                throw new ArgumentException("Not encoded properly.", nameof(Encoded));
 
            bool x0 = (Encoded[ScalarBytes - 1] & 0x80) != 0;
            if (x0)
                Encoded[ScalarBytes - 1] &= 0x7f;
 
            BigInteger y = EllipticCurve.ToInt(Encoded);
            if (y >= Curve.Prime)
                throw new ArgumentException("Not a valid point.", nameof(Encoded));
 
            if (x0)
                Encoded[ScalarBytes - 1] |= 0x80;
 
            BigInteger x = Curve.GetX(y, x0);
 
            return new PointOnCurve(x, y);
        }
 
        public static bool Verify(byte[] Data, byte[] PublicKey, HashFunctionArray HashFunction,
            EdwardsCurveBase Curve, byte[] Signature)
        {
            try
            {
                int ScalarBytes = Signature.Length;
                if ((ScalarBytes & 1) != 0)
                    return false;
 
                ScalarBytes >>= 1;
 
                byte[] R = new byte[ScalarBytes];
                Array.Copy(Signature, 0, R, 0, ScalarBytes);
                PointOnCurve r = Decode(R, Curve);
                byte[] S = new byte[ScalarBytes];
                Array.Copy(Signature, ScalarBytes, S, 0, ScalarBytes);
                BigInteger s = EllipticCurve.ToInt(S);
 
                if (s >= Curve.Order)
                    return false;
 
                int c = Data.Length;
                byte[] Bin = new byte[(ScalarBytes << 1) + c];              // dom2(F, C) = blank string
                Array.Copy(R, 0, Bin, 0, ScalarBytes);
                Array.Copy(PublicKey, 0, Bin, ScalarBytes, ScalarBytes);
                Array.Copy(Data, 0, Bin, ScalarBytes << 1, c);              // PH(M)=M
 
                byte[] h = HashFunction(Bin);
 
                BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
                PointOnCurve P1 = Curve.ScalarMultiplication(s, Curve.BasePoint, false);
                PointOnCurve P2 = Curve.ScalarMultiplication(k, Curve.Decode(PublicKey), false);
                Curve.AddTo(ref P2, r);
 
                P1.Normalize(Curve);
                P2.Normalize(Curve);
 
                return P1.Equals(P2);
            }
            catch (ArgumentException)
            {
                return false;
            }
        }
 
        public static bool Verify(Stream Data, byte[] PublicKey, HashFunctionStream HashFunction,
            EdwardsCurveBase Curve, byte[] Signature)
        {
            try
            {
                int ScalarBytes = Signature.Length;
                if ((ScalarBytes & 1) != 0)
                    return false;
 
                ScalarBytes >>= 1;
 
                byte[] R = new byte[ScalarBytes];
                Array.Copy(Signature, 0, R, 0, ScalarBytes);
                PointOnCurve r = Decode(R, Curve);
                byte[] S = new byte[ScalarBytes];
                Array.Copy(Signature, ScalarBytes, S, 0, ScalarBytes);
                BigInteger s = EllipticCurve.ToInt(S);
                byte[] h;
 
                if (s >= Curve.Order)
                    return false;
 
                using (TemporaryStream TempFile = new TemporaryStream())        // dom2(F, C) = blank string
                {
                    TempFile.Write(R, 0, ScalarBytes);
                    TempFile.Write(PublicKey, 0, ScalarBytes);
 
                    Data.Position = 0;
                    Data.CopyTo(TempFile);                                  // PH(M)=M
 
                    TempFile.Position = 0;
                    h = HashFunction(TempFile);
                }
 
                BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order);
                PointOnCurve P1 = Curve.ScalarMultiplication(s, Curve.BasePoint, false);
                PointOnCurve P2 = Curve.ScalarMultiplication(k, Curve.Decode(PublicKey), false);
                Curve.AddTo(ref P2, r);
 
                P1.Normalize(Curve);
                P2.Normalize(Curve);
 
                return P1.Equals(P2);
            }
            catch (ArgumentException)
            {
                return false;
            }
        }
 
    }
}